Weak pseudocompactness on spaces of continuous functions
The authors analyze, in a purely theoretical setting that lies in the framework of General Topology, a variant of compactness named weak pseudocompactness. Namely, a topological space \(X\) is said to be weakly pseudocompact if it is \(G_\delta\)-dense in at least one of its compactifications. This study is also related to the analysis of continuous extensions of maps between abstract topological spaces. Thus, a space \(X\) satisfies the property \(D_Y\) if for every countable discrete and closed subset \(N\) of \(X\), every function \(f:N \rightarrow Y\) can be continuously extended to a function over all of \(X\) (and with codomain \(Y\)). In the present paper the authors analyze weak pseudocompactness of spaces of continuous functions from a topological space \(X\) into another space \(Y\). Throughout this study the authors relate the results obtained in this setting to the analysis of several completeness properties defined by topological games such as the Banach--Mazur game as well as the Choquet game.
scientific article; zbMATH DE number 6509435
scientific article